Question: Solve for $x$ and $y$ using elimination. ${4x+6y = 58}$ ${-5x-5y = -60}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $4$ ${20x+30y = 290}$ $-20x-20y = -240$ Add the top and bottom equations together. $10y = 50$ $\dfrac{10y}{{10}} = \dfrac{50}{{10}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {4x+6y = 58}\thinspace$ to find $x$ ${4x + 6}{(5)}{= 58}$ $4x+30 = 58$ $4x+30{-30} = 58{-30}$ $4x = 28$ $\dfrac{4x}{{4}} = \dfrac{28}{{4}}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(5)}{= -60}$ ${x = 7}$